Symmetric and Geometric Methods

自古以来，对称在我们的文明中起着无处不在的作用。人类一直被自然界固有的对称之美所吸引，并一直在探索和寻求理解其文化中的含义。这种对对称性的关注导致了丰富的数学理论的发现，这些理论可以解释对称性，并将其应用于从人类学、艺术到工程和科学的大量学科中。本项目建议在科学、艺术和工程中使用对称和几何方法作为主题，开发以主题为导向的课程模块，这些课程模块可以用于振兴数学和其他学科的本科教育。本文建议在这些理论的发现和应用的背景下，揭示和探索其中的一些理论，不断引起人们对伴随直觉推理的定量和定性几何方法的关注。我们可以合理地预期，许多学生将被工程、数学和科学所吸引，因为他们对这些材料的体验。课程模块的实验部分旨在让学生参与探索现代和高级主题，这些主题在当前线性顺序的大学课程中是无法实现的，特别是那些需要先决条件的数学和科学课程。

Symmetry has played a ubiquitous role in our civilization throughout all ages. Mankind has been fascinated by the inherent beauty of symmetry in nature and has explored and searched for understanding its implications in his culture. This preoccupation with symmetry has led to discovery of rich mathematical theories to explain and apply symmetry in a vast number of subjects ranging from anthropology and the arts to engineering and the sciences. This project proposes to use symmetry and geometric methods in the sciences, the arts and engineering as a theme to develop topic-oriented course-modules that can be adapted in revitalizing undergraduate education in mathematics and other subjects. It is proposed to expose and explore some of these theories in their context of discovery and applications, constantly drawing attention to the quantitative and qualitative geometric methods that accompany the intuitive reasoning. It is reasonable to expect that a number of students will be attracted to engineering, mathematics and the sciences through their experience with such material. The proposed lab portion of the course-modules intends to get the students involved hands-on in exploring modern and advanced topics that are inaccessible in the present linearly ordered college curriculum, especially those that requires prerequisites from several mathematics and science courses.